1 code implementation • 28 Aug 2023 • Hong Ye Tan, Stanley Osher, Wuchen Li

The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling.

2 code implementations • 1 Jan 2023 • Hien Dang, Tho Tran, Stanley Osher, Hung Tran-The, Nhat Ho, Tan Nguyen

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing.

1 code implementation • 30 Nov 2022 • Alexander Vidal, Samy Wu Fung, Luis Tenorio, Stanley Osher, Levon Nurbekyan

Instead of tuning $\alpha$, we repeatedly solve the optimization problem for a fixed $\alpha$ effectively performing a JKO update with a time-step $\alpha$.

1 code implementation • 28 Nov 2022 • Khang Nguyen, Hieu Nong, Vinh Nguyen, Nhat Ho, Stanley Osher, Tan Nguyen

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing.

no code implementations • 29 Sep 2022 • Anh Do, Duy Dinh, Tan Nguyen, Khuong Nguyen, Stanley Osher, Nhat Ho

Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function.

no code implementations • 18 May 2022 • Karthik Elamvazhuthi, Bahman Gharesifard, Andrea Bertozzi, Stanley Osher

As a corollary to this result, we establish that the continuity equation of the neural ODE is approximately controllable on the set of compactly supported probability measures that are absolutely continuous with respect to the Lebesgue measure.

no code implementations • 13 Oct 2021 • Bao Wang, Hedi Xia, Tan Nguyen, Stanley Osher

As case studies, we consider how momentum can improve the architecture design for recurrent neural networks (RNNs), neural ordinary differential equations (ODEs), and transformers.

no code implementations • ICLR 2022 • Matthew Thorpe, Tan Minh Nguyen, Hedi Xia, Thomas Strohmer, Andrea Bertozzi, Stanley Osher, Bao Wang

We propose GRAph Neural Diffusion with a source term (GRAND++) for graph deep learning with a limited number of labeled nodes, i. e., low-labeling rate.

1 code implementation • 2 Jun 2021 • Daniel Mckenzie, Howard Heaton, Qiuwei Li, Samy Wu Fung, Stanley Osher, Wotao Yin

Systems of competing agents can often be modeled as games.

2 code implementations • 23 Mar 2021 • Samy Wu Fung, Howard Heaton, Qiuwei Li, Daniel Mckenzie, Stanley Osher, Wotao Yin

Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences.

no code implementations • ICLR 2019 • Alex Tong Lin, Wuchen Li, Stanley Osher, Guido Montufar

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators.

1 code implementation • 9 Nov 2020 • Derek Onken, Levon Nurbekyan, Xingjian Li, Samy Wu Fung, Stanley Osher, Lars Ruthotto

Our approach is grid-free and scales efficiently to dimensions where grids become impractical or infeasible.

Optimization and Control

2 code implementations • 5 Aug 2020 • Howard Heaton, Samy Wu Fung, Alex Tong Lin, Stanley Osher, Wotao Yin

To bridge this gap, we present a new algorithm that takes samples from the manifold of true data as input and outputs an approximation of the projection operator onto this manifold.

no code implementations • 1 May 2020 • Zhicong Liang, Bao Wang, Quanquan Gu, Stanley Osher, Yuan YAO

Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users.

1 code implementation • 4 Dec 2019 • Lars Ruthotto, Stanley Osher, Wuchen Li, Levon Nurbekyan, Samy Wu Fung

State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse-of-dimensionality.

1 code implementation • 2 Nov 2019 • Bao Wang, Difan Zou, Quanquan Gu, Stanley Osher

As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling.

no code implementations • ICLR 2019 • Penghang Yin, Jiancheng Lyu, Shuai Zhang, Stanley Osher, Yingyong Qi, Jack Xin

We prove that if the STE is properly chosen, the expected coarse gradient correlates positively with the population gradient (not available for the training), and its negation is a descent direction for minimizing the population loss.

1 code implementation • 9 Feb 2019 • Wilfrid Gangbo, Wuchen Li, Stanley Osher, Michael Puthawala

We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier.

Optimization and Control

no code implementations • 6 Feb 2019 • Alex Tong Lin, Mark J. Debord, Katia Estabridis, Gary Hewer, Guido Montufar, Stanley Osher

In order to obtain multi-agents that act in a decentralized manner, we introduce a novel algorithm under the popular framework of centralized training, but decentralized execution.

no code implementations • 15 Aug 2018 • Penghang Yin, Shuai Zhang, Jiancheng Lyu, Stanley Osher, Yingyong Qi, Jack Xin

We introduce the notion of coarse gradient and propose the blended coarse gradient descent (BCGD) algorithm, for training fully quantized neural networks.

1 code implementation • 17 Jun 2018 • Stanley Osher, Bao Wang, Penghang Yin, Xiyang Luo, Farzin Barekat, Minh Pham, Alex Lin

We propose a class of very simple modifications of gradient descent and stochastic gradient descent.

2 code implementations • 19 Jan 2018 • Penghang Yin, Shuai Zhang, Jiancheng Lyu, Stanley Osher, Yingyong Qi, Jack Xin

We propose BinaryRelax, a simple two-phase algorithm, for training deep neural networks with quantized weights.

no code implementations • 21 Oct 2017 • Penghang Yin, Minh Pham, Adam Oberman, Stanley Osher

In this paper, we propose an implicit gradient descent algorithm for the classic $k$-means problem.

no code implementations • 17 Apr 2017 • Pratik Chaudhari, Adam Oberman, Stanley Osher, Stefano Soatto, Guillaume Carlier

In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs).

no code implementations • 18 May 2016 • Wei Zhu, Zuoqiang Shi, Stanley Osher

We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images.

no code implementations • 27 Apr 2016 • Wei Zhu, Victoria Chayes, Alexandre Tiard, Stephanie Sanchez, Devin Dahlberg, Andrea L. Bertozzi, Stanley Osher, Dominique Zosso, Da Kuang

In this paper, a graph-based nonlocal total variation method (NLTV) is proposed for unsupervised classification of hyperspectral images (HSI).

no code implementations • 16 Feb 2016 • Da Kuang, Zuoqiang Shi, Stanley Osher, Andrea Bertozzi

We present a new perspective on graph-based methods for collaborative ranking for recommender systems.

no code implementations • 9 Apr 2015 • Fang Li, Stanley Osher, Jing Qin, Ming Yan

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity.

1 code implementation • 30 Jun 2014 • Stanley Osher, Feng Ruan, Jiechao Xiong, Yuan YAO, Wotao Yin

In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics.

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